Julien Lenoir IPAM January 11 th, 2008. Classification Human tissues: Intestines Fallopian tubes...

Julien Lenoir

IPAM January 11th, 2008

Classification Human tissues:

IntestinesFallopian tubesMuscles…

Tools:Surgical threadCatheter, Guide wireCoil…

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Soft-Tissue Simulation

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Intestines simulation [FLMC02]

Goal:Clear the operation field prior to a laparoscopic

intervention Key points:

Not the main focus of the interventionHigh level of interaction with user

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Intestines simulation [FLMC02]Real intestines characteristics: Small intestines (6 m/20 feet) &

Large intestines or colon (1.5 m/5 feet) Huge viscosity (no friction needed) Heterogeneous radius (some bulges) Numerous self contact

Simulated intestines characteristics: Needed:

Dynamic model with high resolution rate for interactivityHigh viscosity (no friction)

Not needed:Torsion (no control due to high viscosity)

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Intestines simulation [FLMC02] Physical modeling: dynamic spline model

Previous work○ [Qin & Terzopoulos TVCG96] “D-NURBS”○ [Rémion et al. WSCG99-00]

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i

i

iiq

EQ

q

E

q

E

dt

d pcc

)(

)(tqi

DOFs = Control points position

pc EE , Kinetic and potential energies

n

ii sbs

1

)()( iqP )(sb Basis spline function (C1, C2…)

○ Similar to an 1D FEM using an high order interpolation function (the basis spline functions)

Lagrangian equations applied to a geometric spline:

Intestines simulation [FLMC02] Physical modeling: dynamic spline model

Using cubic B-spline (C2 continuity)Complexity O(n) due to local property of spline3D DOF => no torsion !

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Potential energies (deformations) = springs

Intestines simulation [FLMC02] Collision and Self-collision model:

Sphere basedBroad phase via a voxel grid

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Extremity of a spline segment

Dynamic distribution (curvilinear distance)

Intestines simulation [FLMC02]

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Dynamic model: Explicit numerical integration (Runge-Kutta 4)

165 control points 72 Hz (14ms computation

time for 1ms virtual) Rendering using

convolution surface or implicit surface


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Fallopian tubes

Avoid intrauterine pregnancy Simulation of salpingectomy Ablation of part/all fallopian tube

Clamp the local areaCut the tissue

Minimally Invasive Surgery (MIS)

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Fallopian tubes

Choice of a predefine cut (not a dynamic cut):3 dynamic splines connected to keep the continuity

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3 dynamic spline models

Constraintsinsuring C2 continuity

Release appropriate constraints to cut

Fallopian tubes

Physical modeling:Dynamic spline modelConstraints handled with Lagrange multipliers +

Baumgarte scheme:○ 3 for each position/tangential/curvature constraint

=> 9 constraints per junction

Fast resolution using a acceleration decomposition:

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EA

BλA

L

LM T

EAA

λA

BA

)( ct

Tc

t

L

LM

M

tT

Tc

t

LLLM

LM

M

AEλ

λA

BA

.

.1

1

Fallopian tubes

Collision and Self-collision with spheres

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Muscles

Dinesh Pai’s workMusculoskeletal strandBased on Strands [Pai02]Cosserat formulation1D model for muscles

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Joey Teran’s workFVM model [Teran et al., SCA03]Invertible element [Irving et al., SCA04]Volumetric model for muscles (3D)

Tool Simulation

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Surgical Thread Simulation Complex and complete behavior

StretchingBendingTorsion

Twist control very important for surgeons

Highly deformable & stiff behavior Highly interactive Suturing, knot tying…

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Surgical Thread Simulation

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Dynamic spline Continuous deformations energies

Continuous stretching [Nocent et al. CAS01]○ Green/Lagrange strain tensor (deformation)○ Piola Kircchoff stress tensor (force)

Continuous bending (approx. using parametric curvature)

No Torsion

[Theetten et al. JCAD07] 4D dynamic spline with full continuous deformations

Surgical Thread SimulationHelpful tool for Suturing

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A new type of constraint for suturing:Sliding constraint:

Allow a 1D model to slide through a specific point (tangent, curvature…can also be controlled)

0),(),,( 0 PtsPtqqg A Usual fixed point constraint

0)),((),,,( 0 PttsPtsqqg Sliding point constraint


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s becomes a new unknown: a free variable

0.

λs

g T

P(s,t)

λ = Force ensuring the constraint g

T

sg

Requires a new equation:Given by the Lagrange multiplier formalism

s(t)


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Resolution acceleration:by giving a direct relation to compute

0.

λs

gs

T

s(t)P(s,t)

λT

sg

s


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Surgical Thread SimulationHelpful tool for knot tying

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Lack of DOF in the knot area:


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Adaptive resolution of the geometry:Exact insertion algorithm (Oslo algorithm):

NUBS of degree d

Knot vectors:

)(sbit it 1it

insertion

)(~sbit~ it

~1~

it 2~

it

i

idjij bb~

,

sinon

~si

0

1 10,

jjjji

ttt

rji

iri

rjrirji

iri

irjrji tt

tt

tt

tt,1

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1,

1,

~

~

~

01,

0,

1 )1( idiii

diii qqq

Simplification is often an approximation


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Results:

Non adaptive dynamic spline Adaptive dynamic spline

Surgical Thread SimulationHelpful tool for cutting

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Useful side effect of the adaptive NUBS:Multiple insertion at the same parametric abscissa

decreases the local continuityLocal C-1 continuity => cut

Tool Simulation

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Catheter/Guidewire navigation

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Interventional neuroradiology Diagnostic:

Catheter/Guidewirenavigation

Therapeutic:CoilStent…


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Arteries/venous network reconstruction

Patient specific datafrom CT scan or MRI

Vincent Luboz’swork at CIMIT/MGH


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Physical modeling of Catheter/Guidewire/Coil:1 mixed deformable object =>

○ Adaptive mechanical properties○ Adaptive rest position

Arteries are not simulated (fixed or animated)

Beam element model (~100 nodes)○ Non linear model (Co-rotational)○ Static resolution:

K(U).U=F1 Newton iteration = linearization


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Contact handling:Mechanics of contact: Signorini’s lawFixed compliance C during 1 time step

=> Delassus operator:

0.0 fd

THCHW

Solving the current contact configuration:Detection collisionLoop until no new contact

○ Use status method to eliminate contacts○ Detection collision

If algorithm diverge, use sub-stepping


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Arteries 1st test:Triangulated surface for contact


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Arteries 2nd test:Convolution surface for

contact f(x)=0○ Based on a skeleton

which can be animatedvery easily and quickly

○ Collision detectionachieve by evaluatingf(x)

○ Collision responsealong f(x)


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Coil deployment:Using the same technique

Others 1D model

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Hair simulation

Florence Bertail’s (PhD06 – SIGGRAPH07) L’Oréal

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Hair simulation

Dynamic model Animated with Lagrange equations Kircchoff constitutive law

Physical DOF (curvatures + torsion)○ Easy to evaluate the deformations energies○ Difficult to reconstruct the geometry:

Super-Helices [Bertails et al., SIGGRAPH06]39

Julien Lenoir IPAM January 11 th, 2008. Classification Human tissues: Intestines Fallopian tubes...

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